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Low energy expansion of the four-particle genus-one amplitude in type II superstring theory

Low energy expansion of the four-particle genus-one amplitude in type II superstring theory,10.1088/1126-6708/2008/02/020,Journal of High Energy Physi

Low energy expansion of the four-particle genus-one amplitude in type II superstring theory   (Citations: 15)
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A diagrammatic expansion of coefficients in the low-momentum expansion of the genus-one four-particle amplitude in type II superstring theory is developed. This is applied to determine coefficients up to order s6 R4 (where s is a Mandelstam invariant and R the linearized super-curvature), and partial results are obtained beyond that order. This involves integrating powers of the scalar propagator on a toroidal world-sheet, as well as integrating over the modulus of the torus. At any given order in s the coefficients of these terms are given by rational numbers multiplying multiple zeta values (or Euler-Zagier sums) that, up to the order studied here, reduce to products of Riemann zeta values. We are careful to disentangle the analytic pieces from logarithmic threshold terms, which involves a discussion of the conditions imposed by unitarity. We further consider the compactification of the amplitude on a circle of radius r, which results in a plethora of terms that are power-behaved in r. These coefficients provide boundary `data' that must be matched by any non-perturbative expression for the low-energy expansion of the four-graviton amplitude. The paper includes an appendix by Don Zagier.
Journal: Journal of High Energy Physics - J HIGH ENERGY PHYS , vol. 2008, no. 02, pp. 020-020, 2008
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    • ...Specific polynomials are listed in table 1 of [7] and earlier in the string literature [9, 10]...
    • ...In our case the polynomials are constrained by Lorentz invariance and particle exchange properties to be the symmetric Pk(s, t, u). It becomes an algebra problem rather than a physics problem to find these polynomials. This problem was studied in [9, 10]...

    Daniel Z. Freedmanet al. The D 2 k R 4 invariants of supergravity

    • ...The α ′ expansion of (3.10) was studied in the papers [44], and the first appearance of two independent structures in D 12 R 4 was noted [45]...
    • ...linear combination is selected by the string amplitude [44, 45]...

    Henriette Elvanget al. A simple approach to counterterms in N=8 supergravity

    • ...dimensional scattering computations [9, 10]...

    Humberto Gomezet al. The overall coefficient of the two-loop superstring amplitude using pu...

    • ...in (3.4). The term in (3.22) involving the tree-level part of E pert,0) is a stringy threshold effect that was discussed in [31]...

    Michael B. Greenet al. String theory dualities and supergravity divergences

    • ...Comparing these coefficients with known ‘data’ from the low-energy expansion of tree-level and genus-one perturbative string theory in nine and ten dimensions [9, 10] shows a surprising degree of agreement...
    • ...Its precise expression, reviewed in [10], has a much more complicated threshold structure but it has the notable property that the scale of the logarithm cancels, using s + t + u = 0...
    • ...In addition to terms that are power-behaved in the radius rA or rB, there are also terms proportional to log rA or log rB. Such terms arise explicitly at genus-one in nine-dimensional string theory [10]...
    • ...For example, there is a term of the form rlog r × s 4 R 4 , which is intimately related to the presence of the genus-one s 4 log s R 4 term in ten dimensions determined in [10]...
    • ...However, after T-duality to the IIA theory, we are able to compare a number of coefficients with those derived explicitly from genus-one in string theory compactified on a circle [10] and find precise agreement...

    Michael B. Greenet al. Modular properties of two-loop maximal supergravity and connections wi...

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